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OPA1656: High-Performance CMOS Audio Op Amp

Excessive output capacitors will be punished by an output voltage noise peak.
Output impedance of opamps and regulators looks slightly inductive, a consequence
of their 6 dB/octave gain drop. Still, the LT30xx family is in a class of it's own, but
if you are after minimum noise, you should damp at least the large capacitors.

The LT3080 looks noisier than it should be. The datasheet says it wants an output capacitor for stability, which the label on the chart does not mention.

The LT3081 datasheet mentions PCB traces (not everyone has the luxury of ground and/or supply planes) having enough inductance to resonate with ceramic caps at high ultrasonic frequencies, so Analog recommend damping the resonance Q with some low-value resistors in the supply lines:

In LT3081 applications with long wires or PCB traces, the
inductive reactance may cause instability. In some cases,
adding series resistance to the input and output lines (as
shown in Figure 4) may sufficiently dampen these possible
high-Q lines and provide stability.

Pages 15 and 16 here: https://www.analog.com/media/en/technical-documentation/data-sheets/3081fc.pdf

1 mm wide PCB traces have very roughly 10 nH of inductance per centimetre, so 10 cm (4 inches) is good for about 100 nH. Your standard opamp bypass 0.1 uF ceramic cap has less than 0.1 ohm ESR, so the Q of the tuned circuit is given by Q = (1/R)*√(L/C), equal to or greater than 10 in this instance. Bumping up the bypass to several uF helps considerably, as does lousing up the Q with suitable series resistors in the supply lines.

My preference is bypassing opamp supply pins with 3 to 10 uF ceramics, not that much more expensive than 0.1 uF parts, fed by series resistors of a few ohms from the rails. That keeps the resonances in line without collapsing the opamp supply too badly: 10 uF is 1 ohm at aout 16 kHz and OPA16xx PSRR is still > 60 or 70 dB there. Say the device is honking out 20 milliamps into a 600 ohm load, that's about 12 volts output. With 1 ohm impedance at the power pins you can expect 20 millivolts of supply bounce, which 60 dB of PSRR knocks down to 20 microvolts at the output pin. But the output is 12 volts, so your contamination is 116 dB below the signal. No big deal. Higher load impedances will improve the ratio, and just for giggles you could bypass the ceramic with a largish electrolytic, say 220 uF, also cheap as chips, to bring the 1 ohm threshold to under 1 kHz where the PSRR will be 30 dB better. Sure it's a big ol' pile of Cs and Rs, but that high performance opamp is six or seven dollars at Mouser so why begrudge another couple bucks for passives?